Bayer's Process for extraction of aluminium

In Bayer's process in the digester both water soluble sodium aluminate and sodium silicate are formed. After that my textbook says cooling the sodium aluminate it crystallizes to to give aluminium hydroxide and sodium hydroxide. My two questions are, one, in the digester alumina reacts with sodium hydroxide to form sodium aluminate and water, but when the heat and pressure are removed why does it give aluminium hydroxide and sodium hydroxide? Why not sodium hydroxide and alumina? And secondly, how is the water containing dissolved sodium aluminate separated from the water containing dissolved sodium silicate?